Abstract: To detect communities in complex networks, a density set algorithm (DSA) is proposed by introducing the concept of density set. The key idea of the algorithm is to constantly construct density sets in a network and decide whether the density set founded later can lead to generate a new community or amalgamate it with an old one. Step by step, the networks with apparent community structure can be partitioned well by the proposed method. The running time of DSA is approximately O(n+m) for a general network and O(n) for a sparse network, where n is the number of nodes and m the number of edges in a network. Tests on three typical real world networks and a benchmark reveal that DSA produces desired results. So the proposal is reasonable, and has the potential for wide applications in physics and computer science.